The VIA Cyrix III, later renamed C3, is an x86 CPU based on a design by Centaur Technology, a former IDT subsidiary and creator of the WinChip C6. VIA bought Centaur from IDT in 1999.
While being much slower than x86 CPUs made by AMD and Intel, VIA designed the chip for the low power segment of the market, and use simplicity in design, to deliver niche qualities which make it attractive to some buyers. Features of the C3 include the lowest manufacturing cost of all modern x86 processors by far and low electrical consumption levels (about 10-30% of a Pentium 4 at comparable speed) and thus low heat output, enabling the processor to run with a passive heatsink cooling solution. In later versions (Nehemiah) it also features a hardware random number generator and very high performance AES encryption in hardware, all packed in a BGA package the size of a 1 cent coin.
VIA initially planned to develop the Cyrix III as a successor to the Cyrix M II, codenamed "Joshua". In the meantime the Centaur team worked on the successor to that, a WinChip 4 core based technology codenamed "Samuel". After many delays, the Joshua project was finally cancelled due to lack of performance and the ahead of schedule Samuel was renamed and released as the Cyrix III in June 2000. However, VIA kept the name of "Cyrix III" in order to avoid wasting the money the company had already spent on the marketing campaign. From a technical point of view, the Cyrix III has nothing to do with Cyrix anymore.
References:
Introduction Press ReleaseVIA Cyrix III site 2000VIA C3 site 2005Cyrix III review on tecchannel.de

By 2001, the Samuel 2 (C5B) was released, this time just as the VIA C3. Samuel 2 ran at a higher clock speed and added a level 2 cache, required lower voltage and was also available in an Enhanced Ball Grid Array (EBGA) version. EBGA allowed the CPU to be mounted directly onto a motherboard without using Intel's costly Socket 370.
This is a Samuel 2 Engineering Sample, still marked Cyrix III and in PGA package.